The ferroelectricity of the ilmenite structure minerals lithium tantalate and lithium niobate is studied theoretically, using the method recently introduced by Slater for barium titanate. The metal ions are assumed to move in a potential which has small quartic terms as well as the usual quadratic terms, all satisfying the appropriate crystal symmetry requirements. This results in a slight dependence of the ionic-displacement polarizability of each metal ion on both the temperature and the polarization of the crystal. The local electric field strength is computed exactly for each ion by Ewald's method, and the internal field constants are given for a number of positions in a rhombohedral unit cell of axial angle $\ensuremath{\alpha}={56}^{\ensuremath{\circ}}$. The polarizabilities can be estimated from other crystal polarization data, leading to a spontaneous polarization below the upper Curie temperature ${T}_{0}$ of $2{({T}_{0}\ensuremath{-}T)}^{\frac{1}{2}}$ microcoulombs ${\mathrm{cm}}^{\ensuremath{-}2}$ (without electromechanical correction). Whereas in barium titanate all dipole moments are in the direction of the resultant polarization, it is found here that the lower crystal symmetry results in sizeable components of the oxygen dipole moments perpendicular to the total polarization, but these last components produce a large field in the direction of the polarization at other ionic positions.